Quantum computing approach to realistic ESG-friendly stock portfolios

ArXiv ID: 2404.02582 “View on arXiv”

Authors: Unknown

Abstract

Finding an optimal balance between risk and returns in investment portfolios is a central challenge in quantitative finance, often addressed through Markowitz portfolio theory (MPT). While traditional portfolio optimization is carried out in a continuous fashion, as if stocks could be bought in fractional increments, practical implementations often resort to approximations, as fractional stocks are typically not tradeable. While these approximations are effective for large investment budgets, they deteriorate as budgets decrease. To alleviate this issue, a discrete Markowitz portfolio theory (DMPT) with finite budgets and integer stock weights can be formulated, but results in a non-polynomial (NP)-hard problem. Recent progress in quantum processing units (QPUs), including quantum annealers, makes solving DMPT problems feasible. Our study explores portfolio optimization on quantum annealers, establishing a mapping between continuous and discrete Markowitz portfolio theories. We find that correctly normalized discrete portfolios converge to continuous solutions as budgets increase. Our DMPT implementation provides efficient frontier solutions, outperforming traditional rounding methods, even for moderate budgets. Responding to the demand for environmentally and socially responsible investments, we enhance our discrete portfolio optimization with ESG (environmental, social, governance) ratings for EURO STOXX 50 index stocks. We introduce a utility function incorporating ESG ratings to balance risk, return, and ESG-friendliness, and discuss implications for ESG-aware investors.

Keywords: Portfolio Optimization, Quantum Annealing, Markowitz Portfolio Theory, ESG Ratings, Discrete Optimization, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematics including non-polynomial hard optimization, Markowitz theory extensions, and convex optimization, but its empirical implementation is limited to theoretical mapping and conceptual ESG utility functions without reported backtests or dataset specifics.

  flowchart TD
    A["Research Goal:<br>Discrete ESG Portfolio Optimization<br>via Quantum Annealing"] --> B["Methodology:<br>Discrete Markowitz Theory<br>vs. Continuous MPT"]
    B --> C["Inputs:<br>EURO STOXX 50 Stocks<br>Risk/Return Data + ESG Ratings"]
    C --> D{"Computation:<br>Quantum Annealer (QPU)"}
    D --> E["Output:<br>Efficient Frontier<br>with Integer Weights"]
    E --> F["Key Findings:<br>1. Discrete converges to Continuous<br>2. Outperforms rounding methods<br>3. ESG-Utility Function viable"]